Solve the following inequality for qq. Write your answer in simplest form.
8, q, plus, 5, is less than or equal to, 4, q, plus, 10
8q+5≤
4q+10

Let's solve the inequality \( 8q + 5 \leq 4q + 10 \) for \( q \).

### Step 1: Subtract \( 4q \) from both sides.
\[
8q + 5 - 4q \leq 4q + 10 - 4q
\]
\[
4q + 5 \leq 10
\]

### Step 2: Subtract 5 from both sides.
\[
4q + 5 - 5 \leq 10 - 5
\]
\[
4q \leq 5
\]

### Step 3: Divide both sides by 4 to solve for \( q \).
\[
q \leq \frac{5}{4}
\]

### Final Answer:
The solution to the inequality is \( q \leq \frac{5}{4} \).

Would you like further details on any of the steps? Here are five related questions you can explore:

1. How do you solve a linear inequality with two variables?
2. What are the rules for adding and subtracting inequalities?
3. How do you graph the solution of a linear inequality?
4. What is the difference between solving an equation and an inequality?
5. Can an inequality have multiple solutions?

**Tip:** When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.

Solve the following inequality for q. Write your answer in simplest form: 8q + 5 ≤ 4q + 10

Discover how to solve the linear inequality 8q + 5 ≤ 4q + 10 with a step-by-step explanation. This problem focuses on key algebraic concepts, including the manipulation of inequalities and properties of inequalities. Ideal for students in Grades 7-9.

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